Results 141 to 150 of about 466,881 (179)

A Prime Submodule Principle

Algebra Colloquium, 2014
In this paper, we extend the concept of Ako and Oka families to submodules, study the behavior of the extended prime submodule principle and use these concepts to give new proofs of some familiar theorems.
Nekooei, R., Rostami, E.
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Spectrum of prime -submodules

Fuzzy Sets and Systems, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reza Ameri, R. Mahjoob
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ON CHARACTERIZATIONS OF PRIME AND ALMOST PRIME SUBMODULES

JP Journal of Algebra, Number Theory and Applications, 2018
Summary: We focus on some notions of prime submodules over a commutative ring with identity. Suppose \(R\) is a commutative ring with identity and \(M\) is an \(R\)-module. For more generalized version of prime module, we have weakly and almost prime submodules by defining different sets that contain the multiplication between element of ring and ...
Steven, Irawati
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On almost \(S\)-prime submodules

2023
Let \(R\) be a commutative ring with non-zero identity, \(S\subseteq R\) be a multiplicatively closed subset of \(R\) and let \(M\) be an \(R\)-module. The purpose of the paper under review is to introduce and investigate of the notion of almost \(S\)-prime submodules. A submodule \(N\) of \(M\) with \((N :_R M)\cap S =\emptyset\); is said to be almost
Farzalipour, F., Ghaseminejad, R., Sayedsadeghi, M. S.   +2 more
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On the uniqueness of almost prime submodules within cyclic uniserial modules

Journal of Discrete Mathematical Sciences and Cryptography
A uniserial module is a module that satisfies both ascending chain condition and descending chain condition, which makes a uniserial module an Artinian module and a Noetherian module at the same time.
I. G. A. W. Wardhana, Fariz Maulana, N. Sarmin   +2 more
semanticscholar   +1 more source

On S-1-absorbing prime submodules

, 2021
Let [Formula: see text] be a commutative ring with non-zero identity, [Formula: see text] a multiplicatively closed subset of [Formula: see text] and [Formula: see text] a unital [Formula: see text]-module.
F. Farzalipour, P. Ghiasvand
semanticscholar   +1 more source

SOME ASPECTS OF ROUGHLY PRIME SUBMODULES

South East Asian J. of Mathematics and Mathematical Sciences
Let R be a commutative ring with unity and M be an R-module. The aim of this article is to introduce and investigate certain properties of a new notion of prime submodules of a module, namely roughly prime submodules.
H. Saharia, Helen K. Saikia
semanticscholar   +1 more source

On the Dual Notion of Prime Submodules

Algebra Colloquium, 2012
Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of prime submodules (that is, second submodules of M) and investigate the conditions under which the number of maximal second submodules of M is finite. Furthermore, we introduce the concept of coisolated submodules of M and obtain some related characterizations.
Ansari-Toroghy, H., Farshadifar, F.
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Totally σ–prime ideals and submodules

Communications in Algebra
Let A be a commutative ring and σ be a hereditary torsion theory in Mod−A. We introduce the concept of a totally σ–prime ideal, which is a generalization of prime and σ–prime ideals, and extend it to consider also submodules instead of ideals. The use of
F. Omar, P. Jara
semanticscholar   +1 more source

Nil Versions of Prime Submodules

Asian-European Journal of Mathematics
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be an [Formula: see text]-module. A proper submodule [Formula: see text] of [Formula: see text] is said to be prime if for any [Formula: see text] and [Formula: see text]
F. Farshadifar
semanticscholar   +1 more source